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Matrices · Form 5

Matrices: Worked Examples (Easier)

Builds the basics: reading a matrix's order, adding or subtracting matrices of the same order, scalar multiplication, and finding the determinant of a 2×2 matrix. Ideal for students just starting the chapter.

Written by the spmmath.com.my editorial team.

Worked example 1

Given A = [[7, 2], [−3, 5]] and B = [[4, 6], [−1, 2]], state the order of A, then find A − B.

  1. A has 2 rows and 2 columns, so the order of A is 2 × 2.
  2. Subtract entry by entry (same position): [[7−4, 2−6], [−3−(−1), 5−2]].
  3. Simplify each entry: [[3, −4], [−2, 3]].

Worked example 2

Find 4M where M = [[−2, 3], [5, −1]].

  1. Scalar multiplication multiplies every entry by 4.
  2. 4M = [[4×(−2), 4×3], [4×5, 4×(−1)]].
  3. Compute: [[−8, 12], [20, −4]].

Worked example 3

Find the determinant of M = [[6, 4], [3, 5]].

  1. For [[a, b], [c, d]], the determinant is ad − bc.
  2. Here a=6, b=4, c=3, d=5, so det M = (6×5) − (4×3).
  3. det M = 30 − 12 = 18.

Worked example 4

Given A = [[3, −2], [4, 1]] and B = [[5, 6], [−2, 0]], find A + B.

  1. Add corresponding elements.
  2. Row 1: [3 + 5, −2 + 6] = [8, 4].
  3. Row 2: [4 + (−2), 1 + 0] = [2, 1].

Worked example 5

Find the determinant of the matrix [[8, 3], [2, 7]].

  1. For [[a, b], [c, d]], determinant = ad − bc.
  2. Substitute: (8 × 7) − (3 × 2).
  3. Calculate: 56 − 6 = 50.

Worked example 6

Given N = [[1, −5], [−2, 4]], find 3N.

  1. Multiply every element by 3.
  2. Row 1: [3 × 1, 3 × (−5)] = [3, −15].
  3. Row 2: [3 × (−2), 3 × 4] = [−6, 12].

Worked example 7

Given A = [[9, −2], [0, 6]], state the order of A, then find 5A.

  1. A has 2 rows and 2 columns, so the order of A is 2 × 2.
  2. Multiply every entry of A by 5.
  3. 5A = [[5×9, 5×(−2)], [5×0, 5×6]].
  4. 5A = [[45, −10], [0, 30]].

Worked example 8

Find the determinant of the matrix R = [[2, 9], [4, 5]].

  1. For [[a, b], [c, d]], the determinant is ad − bc.
  2. det R = (2 × 5) − (9 × 4).
  3. det R = 10 − 36.
  4. det R = −26.

Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)

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Frequently asked questions

What basic matrix skills do these easy questions test?

Easy-level matrix questions check whether you can write down the order of a matrix, add or subtract matrices of the same order, multiply a matrix by a scalar, and multiply two matrices correctly. Get comfortable identifying rows and columns first, most early mistakes come from mismatching matrix orders before doing any arithmetic.

Why do students lose marks even when the final answer is correct?

Markers want to see each step of the matrix operation, not just the final matrix. Skipping the row-by-column working for multiplication, or not stating the order of the resulting matrix, can cost method marks even if the numbers end up right.

Always write out each entry's calculation clearly.

What is the most common error when multiplying two matrices?

Students often multiply matrices in the wrong order or try to multiply matrices whose dimensions don't match (columns of the first must equal rows of the second). Before multiplying, check the orders line up, and remember matrix multiplication is generally not commutative, AB and BA can give different results.

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